What was one place on the globe where the Cold War was "hot" and U.S. soldiers fought and died?
US soldiers fought and died both in the Korean War in the early 50's and in Vietnam from the early 60's until 1973.
In both cases the countries had been partitioned into north and south, with the north being supported by communist governments and the south supported by the US and some of her allies, e.g. Britain and Australia.
If we define the Cold War as being the conflict between the USA and Soviet Union for ideological, strategic and military dominance, then neither of these involved direct conflict with Soviet troops.
In the case of Korea it did mean direct conflict with communist Chinese troops. In Vietnam, North Vietnam received extensive military aid from the Soviets in their conflict with both the south and the USA.
In both cases it was a confrontation between the USA and communism, both directly and by proxy.